[latexpage]
\nAt first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\n\\[
\nf_k = f(x_k),\\: x_k = x^*+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}
\n\\]
\nwhere !$h$ is some step.
\nThen we interpolate points $\\{(x_k,f_k)\\}$ by polynomial
\n\\begin{equation} \\label{eq:poly}
\nP_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}
\n\\end{equation}
\nIts coefficients !$\\{a_j\\}$ are found as a solution of system of linear equations:
\n\\begin{equation} \\label{eq:sys}
\n\\left\\{ P_{N-1}(x_k) = f_k\\right\\},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}
\n\\end{equation}
\nHere are references to existing equations: (\\ref{eq:poly}), (\\ref{eq:sys}).
\nHere is reference to non-existing equation (\\ref{eq:unknown}).<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
[latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$: \\[ f_k = f(x_k),\\: x_k = x^*+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2} \\] where !$h$ is some step. Then we interpolate points $\\{(x_k,f_k)\\}$ by polynomial \\begin{equation} … <\/p>\n